et R be the region between the curves defined by the functions y = x2 and y = 6−x on the interval [−3, 2]. A graph of these two functions and the x- and y-axes is shown above.    Use definite integrals and cylindrical shells to find volumes . Set up, but do not evaluate, a definite integral for the volume of the solid obtained by rotating R about the line x = −3. Showing your work: Draw a typical approximating rectangle of R and the result of revolving this approximating rectangle about the axis of rotation. Find the volume of this cylindrical shell.

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